Is it possible to build an AGI with neural networks on neuromorphic chips?
No. The reasons include but are not limited to:

lack of understanding of how the brain works

current ANNs are mostly good at pattern recognition and generative   tasks, but lack the capacity to create abstractions on their own

we can't match the size/number of artificial neurons to the number of biological neurons

even with a much smaller ANN size, performance is an issue (i.e. state of the art image categorization ANNs have to be trained few weeks on multi GPU rigs to match human level).